LSU 06/04/2007Electronics 71 Analog to Digital Converters Electronics Unit – Lecture 7 Representing a continuously varying physical quantity by a sequence of discrete numerical values

LSU 06/04/2007Electronics 72 Conversion Methods (selected types, there are others) Ladder Comparison Successive Approximation Slope Integration Flash Comparison

LSU 06/04/2007Electronics 73 Ladder Comparison

LSU 06/04/2007Electronics 74 Single slope integration Charge a capacitor at constant current Count clock ticks Stop when the capacitor voltage matches the input Cannot achieve high resolution –Capacitor and/or comparator - + IN C R S Enable N-bit Output Q Oscillator Clk Counter Start Conversion Vin Counting time

LSU 06/04/2007Electronics 75 Successive Approximation

LSU 06/04/2007Electronics 76 Flash Comparison If N is the number of bits in the output word…. Then 2 N comparators will be required. With modern microelectronics this is quite possible, but will be expensive.

LSU 06/04/2007Electronics 77 Pro and Cons Slope Integration & Ladder Approximation Cheap but Slow

LSU 06/04/2007Electronics 78 Pro and Cons Flash Comparison Fast but Expensive Slope Integration & Ladder Approximation Cheap but Slow

LSU 06/04/2007Electronics 79 Pro and Cons Successive Approximation The Happy Medium ?? Slope Integration & Ladder Approximation Cheap but Slow Flash Comparison Fast but Expensive

LSU 06/04/2007Electronics 710 Resolution Suppose a binary number with N bits is to represent an analog value ranging from 0 to A There are 2 N possible numbers Resolution = A / 2 N

LSU 06/04/2007Electronics 711 Resolution Example Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with an 8-bit A/D converter 2.5 / 2 8 = V, or about 10 mV per step 300 K / 2 8 = 1.2 K per step

LSU 06/04/2007Electronics 712 Resolution Example Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with a 10-bit A/D converter 2.5 / 2 10 = V, or about 2.4 mV per step 300 K / 2 10 = 0.29 K per step Is the noise present in the system well below 2.4 mV ?

LSU 06/04/2007Electronics 713 Quantization Noise Each conversion has an average uncertainty of one- half of the step size ½(A / 2 N ) This quantization error places an upper limit on the signal to noise ratio that can be realized. Maximum (ideal) SNR ≈ 6 N decibels ( N = # bits ) e.g. 8 bit → 49.8 db, 10 bit → 61.8 db

LSU 06/04/2007Electronics 714 Signal to Noise Ratio Recovering a signal masked by noise Some audio examples In each successive example the noise power is reduced by a factor of two (3 db reduction), thus increasing the signal to noise ratio by 3 db each time. Example 1Example 2Example 3Example 4

LSU 06/04/2007Electronics 715 Conversion Time Time required to acquire a sample of the analog signal and determine the numerical representation. Sets the upper limit on the sampling frequency. For the A/D on the BalloonSat board, T C ≈ 32 μs, So the sampling rate cannot exceed about 30,000 samples per second (neglecting program overhead)

LSU 06/04/2007Electronics 716 Data Collection – Sampling Rate The Nyquist Rate A signal must be sampled at a rate at least twice that of the highest frequency component that must be reproduced. Example – Hi-Fi sound (20-20,000 Hz) is generally sampled at about 44 kHz. External temperature during flight need only be sampled every few seconds at most.

LSU 06/04/2007Electronics 717 Activity E7a Do the HuSAC ® a party game for techies... Hu man S uccessive A pproximation C onverter

LSU 06/04/2007Electronics 718 Activity Data Acquisition Using BalloonSat